Step 1 :
Divide $ 6515 $ by $ 756 $ and get the remainder

$$ 6515 : 756 = 8 \text{ ( remainder is } \color{blue}{ 467 } \text{ ) } $$

The remainder is positive ($ 467 > 0 $), so we will continue with division.

Step 2 :
Divide $ 756 $ by $ \color{blue}{ 467 } $ and get the remainder

$$ 756 : 467 = 1 \text{ ( remainder is } \color{blue}{ 289 } \text{ ) } $$

The remainder is still positive ($ 289 > 0 $), so we will continue with division.

Step 3 :
Divide $ 467 $ by $ \color{blue}{ 289 } $ and get the remainder

$$ 467 : 289 = 1 \text{ ( remainder is } \color{blue}{ 178 } \text{ ) } $$

The remainder is still positive ($ 178 > 0 $), so we will continue with division.

Step 4 :
Divide $ 289 $ by $ \color{blue}{ 178 } $ and get the remainder

$$ 289 : 178 = 1 \text{ ( remainder is } \color{blue}{ 111 } \text{ ) } $$

The remainder is still positive ($ 111 > 0 $), so we will continue with division.

Step 5 :
Divide $ 178 $ by $ \color{blue}{ 111 } $ and get the remainder

$$ 178 : 111 = 1 \text{ ( remainder is } \color{blue}{ 67 } \text{ ) } $$

The remainder is still positive ($ 67 > 0 $), so we will continue with division.

Step 6 :
Divide $ 111 $ by $ \color{blue}{ 67 } $ and get the remainder

$$ 111 : 67 = 1 \text{ ( remainder is } \color{blue}{ 44 } \text{ ) } $$

The remainder is still positive ($ 44 > 0 $), so we will continue with division.

Step 7 :
Divide $ 67 $ by $ \color{blue}{ 44 } $ and get the remainder

$$ 67 : 44 = 1 \text{ ( remainder is } \color{blue}{ 23 } \text{ ) } $$

The remainder is still positive ($ 23 > 0 $), so we will continue with division.

Step 8 :
Divide $ 44 $ by $ \color{blue}{ 23 } $ and get the remainder

$$ 44 : 23 = 1 \text{ ( remainder is } \color{blue}{ 21 } \text{ ) } $$

The remainder is still positive ($ 21 > 0 $), so we will continue with division.

Step 9 :
Divide $ 23 $ by $ \color{blue}{ 21 } $ and get the remainder

$$ 23 : 21 = 1 \text{ ( remainder is } \color{blue}{ 2 } \text{ ) } $$

The remainder is still positive ($ 2 > 0 $), so we will continue with division.

Step 10 :
Divide $ 21 $ by $ \color{blue}{ 2 } $ and get the remainder

$$ 21 : 2 = 10 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

The remainder is still positive ($ 1 > 0 $), so we will continue with division.

Step 11 :
Divide $ 2 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 2 : \color{blue}{ \boxed { 1 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 1 }} $.

This solution can be visualized using a Venn diagram.

The GCD equals the product of the numbers at the intersection.

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